export supnorm, @_isdefined


"""
    refine(tt, n) 

Refine range by decreasing stepsize by a factor `n`.
"""
refine(tt, n) =  first(tt):(Base.step(tt)/n):last(tt)


"""
    runmean(x)

Running mean of the vector `x`.
"""
runmean(x, cx = cumsum(x)) = [cx[n]/n for n in 1:length(x)]

function runmean(xx::Matrix) 
    yy = copy(xx) / 1
    m = 0 * (copy(xx[1,:])/1)
    for i in 1:size(yy, 1)
        m[:] = m + (xx[i, :] - m)/i
        yy[i, :] = m
    end
    yy
end

"""
    cumsum0(x)

Cumulative sum starting at 0 such that `cumsum0(diff(x)) ≈ x`.
"""
function cumsum0(dx::Vector)
        n = length(dx) + 1
        x = similar(dx, n)
        x[1] = 0.0      
        for i in 2:n
                x[i] = x[i-1] + dx[i-1] 
        end
        x
end

supnorm(x) = sum(abs.(x))

macro _isdefined(var)
    quote
        try local _ = $(esc(var))
            true
        catch err
            isa(err, UndefVarError) ? false : rethrow(err)
        end
    end
end

if isempty(methods(chol, (UniformScaling,)))
    include("chol.jl")
end

"""
    outer(x[, y])
    
Short-hand for quadratic form xx' (or xy').
"""
outer(x) = x*x'
outer(x,y) = x*y'

"""
    inner(x[, y])

Short-hand for quadratic form x'x (or x'y).
"""
inner(x) = dot(x,x)
inner(x,y) = dot(x,y)


"""
    mat(yy::Vector{SVector})

Reinterpret `X` or `yy` to an array without change in memory.
"""
mat(yy::Vector{SVector{d,T}}) where {d,T} = reshape(reinterpret(T, yy), d, length(yy))

unmat(A::Matrix{T}) where {T} = reinterpret(SVector{size(A, 1), T}, A, (size(A, 2),))
unmat(::Type{SVector{d,T}}, A::Matrix{T}) where {d,T} = reinterpret(SVector{d,T}, A, (div(length(A), d),))


"""
    quaternion(m::SMatrix{3,3})

Compute the (rotation-) quarternion of a 3x3 rotation matrix. Useful to create
isodensity ellipses from spheres in GL visualizations.
"""
function quaternion(m)
    qw2 = 1 + m[1,1] + m[2,2] + m[3,3]
    if qw2 < 0
        #if abs(det(m) - 1) < sqrt(eps()) # might fail with svd() for any reasonable values of `eps`
            qw2 = -qw2
        #else
        #    throw(DomainError())
        #end
    end

    qw = sqrt(qw2)/2
    qx = (m[3,2] - m[2,3])/(4qw)
    qy = (m[1,3] - m[3,1])/(4qw)
    qz = (m[2,1] - m[1,2])/(4qw)
    SVector{4}(qx,qy,qz,qw)
end

"""
    piecewise(X::SamplePath) -> tt, xx

If X is a jump process with piecewise constant paths and jumps in `X.tt`,
piecewise returns coordinates path for plotting purposes.
"""
function piecewise(Y::SamplePath)
    tt = [0.0]
    append!(tt, repeat(Y.tt[2:end], inner=2))
    push!(tt, Y.tt[end])
    tt, repeat(Y.yy, inner=2)
end


"""
    _viridis

Color data of the Viridis map by Nathaniel J. Smith, Stefan van Der Walt, Eric Firing
from https://github.com/BIDS/colormap/blob/master/colormaps.py .
"""
_viridis = [[0.267004, 0.004874, 0.329415],
[0.268510, 0.009605, 0.335427],
[0.269944, 0.014625, 0.341379],
[0.271305, 0.019942, 0.347269],
[0.272594, 0.025563, 0.353093],
[0.273809, 0.031497, 0.358853],
[0.274952, 0.037752, 0.364543],
[0.276022, 0.044167, 0.370164],
[0.277018, 0.050344, 0.375715],
[0.277941, 0.056324, 0.381191],
[0.278791, 0.062145, 0.386592],
[0.279566, 0.067836, 0.391917],
[0.280267, 0.073417, 0.397163],
[0.280894, 0.078907, 0.402329],
[0.281446, 0.084320, 0.407414],
[0.281924, 0.089666, 0.412415],
[0.282327, 0.094955, 0.417331],
[0.282656, 0.100196, 0.422160],
[0.282910, 0.105393, 0.426902],
[0.283091, 0.110553, 0.431554],
[0.283197, 0.115680, 0.436115],
[0.283229, 0.120777, 0.440584],
[0.283187, 0.125848, 0.444960],
[0.283072, 0.130895, 0.449241],
[0.282884, 0.135920, 0.453427],
[0.282623, 0.140926, 0.457517],
[0.282290, 0.145912, 0.461510],
[0.281887, 0.150881, 0.465405],
[0.281412, 0.155834, 0.469201],
[0.280868, 0.160771, 0.472899],
[0.280255, 0.165693, 0.476498],
[0.279574, 0.170599, 0.479997],
[0.278826, 0.175490, 0.483397],
[0.278012, 0.180367, 0.486697],
[0.277134, 0.185228, 0.489898],
[0.276194, 0.190074, 0.493001],
[0.275191, 0.194905, 0.496005],
[0.274128, 0.199721, 0.498911],
[0.273006, 0.204520, 0.501721],
[0.271828, 0.209303, 0.504434],
[0.270595, 0.214069, 0.507052],
[0.269308, 0.218818, 0.509577],
[0.267968, 0.223549, 0.512008],
[0.266580, 0.228262, 0.514349],
[0.265145, 0.232956, 0.516599],
[0.263663, 0.237631, 0.518762],
[0.262138, 0.242286, 0.520837],
[0.260571, 0.246922, 0.522828],
[0.258965, 0.251537, 0.524736],
[0.257322, 0.256130, 0.526563],
[0.255645, 0.260703, 0.528312],
[0.253935, 0.265254, 0.529983],
[0.252194, 0.269783, 0.531579],
[0.250425, 0.274290, 0.533103],
[0.248629, 0.278775, 0.534556],
[0.246811, 0.283237, 0.535941],
[0.244972, 0.287675, 0.537260],
[0.243113, 0.292092, 0.538516],
[0.241237, 0.296485, 0.539709],
[0.239346, 0.300855, 0.540844],
[0.237441, 0.305202, 0.541921],
[0.235526, 0.309527, 0.542944],
[0.233603, 0.313828, 0.543914],
[0.231674, 0.318106, 0.544834],
[0.229739, 0.322361, 0.545706],
[0.227802, 0.326594, 0.546532],
[0.225863, 0.330805, 0.547314],
[0.223925, 0.334994, 0.548053],
[0.221989, 0.339161, 0.548752],
[0.220057, 0.343307, 0.549413],
[0.218130, 0.347432, 0.550038],
[0.216210, 0.351535, 0.550627],
[0.214298, 0.355619, 0.551184],
[0.212395, 0.359683, 0.551710],
[0.210503, 0.363727, 0.552206],
[0.208623, 0.367752, 0.552675],
[0.206756, 0.371758, 0.553117],
[0.204903, 0.375746, 0.553533],
[0.203063, 0.379716, 0.553925],
[0.201239, 0.383670, 0.554294],
[0.199430, 0.387607, 0.554642],
[0.197636, 0.391528, 0.554969],
[0.195860, 0.395433, 0.555276],
[0.194100, 0.399323, 0.555565],
[0.192357, 0.403199, 0.555836],
[0.190631, 0.407061, 0.556089],
[0.188923, 0.410910, 0.556326],
[0.187231, 0.414746, 0.556547],
[0.185556, 0.418570, 0.556753],
[0.183898, 0.422383, 0.556944],
[0.182256, 0.426184, 0.557120],
[0.180629, 0.429975, 0.557282],
[0.179019, 0.433756, 0.557430],
[0.177423, 0.437527, 0.557565],
[0.175841, 0.441290, 0.557685],
[0.174274, 0.445044, 0.557792],
[0.172719, 0.448791, 0.557885],
[0.171176, 0.452530, 0.557965],
[0.169646, 0.456262, 0.558030],
[0.168126, 0.459988, 0.558082],
[0.166617, 0.463708, 0.558119],
[0.165117, 0.467423, 0.558141],
[0.163625, 0.471133, 0.558148],
[0.162142, 0.474838, 0.558140],
[0.160665, 0.478540, 0.558115],
[0.159194, 0.482237, 0.558073],
[0.157729, 0.485932, 0.558013],
[0.156270, 0.489624, 0.557936],
[0.154815, 0.493313, 0.557840],
[0.153364, 0.497000, 0.557724],
[0.151918, 0.500685, 0.557587],
[0.150476, 0.504369, 0.557430],
[0.149039, 0.508051, 0.557250],
[0.147607, 0.511733, 0.557049],
[0.146180, 0.515413, 0.556823],
[0.144759, 0.519093, 0.556572],
[0.143343, 0.522773, 0.556295],
[0.141935, 0.526453, 0.555991],
[0.140536, 0.530132, 0.555659],
[0.139147, 0.533812, 0.555298],
[0.137770, 0.537492, 0.554906],
[0.136408, 0.541173, 0.554483],
[0.135066, 0.544853, 0.554029],
[0.133743, 0.548535, 0.553541],
[0.132444, 0.552216, 0.553018],
[0.131172, 0.555899, 0.552459],
[0.129933, 0.559582, 0.551864],
[0.128729, 0.563265, 0.551229],
[0.127568, 0.566949, 0.550556],
[0.126453, 0.570633, 0.549841],
[0.125394, 0.574318, 0.549086],
[0.124395, 0.578002, 0.548287],
[0.123463, 0.581687, 0.547445],
[0.122606, 0.585371, 0.546557],
[0.121831, 0.589055, 0.545623],
[0.121148, 0.592739, 0.544641],
[0.120565, 0.596422, 0.543611],
[0.120092, 0.600104, 0.542530],
[0.119738, 0.603785, 0.541400],
[0.119512, 0.607464, 0.540218],
[0.119423, 0.611141, 0.538982],
[0.119483, 0.614817, 0.537692],
[0.119699, 0.618490, 0.536347],
[0.120081, 0.622161, 0.534946],
[0.120638, 0.625828, 0.533488],
[0.121380, 0.629492, 0.531973],
[0.122312, 0.633153, 0.530398],
[0.123444, 0.636809, 0.528763],
[0.124780, 0.640461, 0.527068],
[0.126326, 0.644107, 0.525311],
[0.128087, 0.647749, 0.523491],
[0.130067, 0.651384, 0.521608],
[0.132268, 0.655014, 0.519661],
[0.134692, 0.658636, 0.517649],
[0.137339, 0.662252, 0.515571],
[0.140210, 0.665859, 0.513427],
[0.143303, 0.669459, 0.511215],
[0.146616, 0.673050, 0.508936],
[0.150148, 0.676631, 0.506589],
[0.153894, 0.680203, 0.504172],
[0.157851, 0.683765, 0.501686],
[0.162016, 0.687316, 0.499129],
[0.166383, 0.690856, 0.496502],
[0.170948, 0.694384, 0.493803],
[0.175707, 0.697900, 0.491033],
[0.180653, 0.701402, 0.488189],
[0.185783, 0.704891, 0.485273],
[0.191090, 0.708366, 0.482284],
[0.196571, 0.711827, 0.479221],
[0.202219, 0.715272, 0.476084],
[0.208030, 0.718701, 0.472873],
[0.214000, 0.722114, 0.469588],
[0.220124, 0.725509, 0.466226],
[0.226397, 0.728888, 0.462789],
[0.232815, 0.732247, 0.459277],
[0.239374, 0.735588, 0.455688],
[0.246070, 0.738910, 0.452024],
[0.252899, 0.742211, 0.448284],
[0.259857, 0.745492, 0.444467],
[0.266941, 0.748751, 0.440573],
[0.274149, 0.751988, 0.436601],
[0.281477, 0.755203, 0.432552],
[0.288921, 0.758394, 0.428426],
[0.296479, 0.761561, 0.424223],
[0.304148, 0.764704, 0.419943],
[0.311925, 0.767822, 0.415586],
[0.319809, 0.770914, 0.411152],
[0.327796, 0.773980, 0.406640],
[0.335885, 0.777018, 0.402049],
[0.344074, 0.780029, 0.397381],
[0.352360, 0.783011, 0.392636],
[0.360741, 0.785964, 0.387814],
[0.369214, 0.788888, 0.382914],
[0.377779, 0.791781, 0.377939],
[0.386433, 0.794644, 0.372886],
[0.395174, 0.797475, 0.367757],
[0.404001, 0.800275, 0.362552],
[0.412913, 0.803041, 0.357269],
[0.421908, 0.805774, 0.351910],
[0.430983, 0.808473, 0.346476],
[0.440137, 0.811138, 0.340967],
[0.449368, 0.813768, 0.335384],
[0.458674, 0.816363, 0.329727],
[0.468053, 0.818921, 0.323998],
[0.477504, 0.821444, 0.318195],
[0.487026, 0.823929, 0.312321],
[0.496615, 0.826376, 0.306377],
[0.506271, 0.828786, 0.300362],
[0.515992, 0.831158, 0.294279],
[0.525776, 0.833491, 0.288127],
[0.535621, 0.835785, 0.281908],
[0.545524, 0.838039, 0.275626],
[0.555484, 0.840254, 0.269281],
[0.565498, 0.842430, 0.262877],
[0.575563, 0.844566, 0.256415],
[0.585678, 0.846661, 0.249897],
[0.595839, 0.848717, 0.243329],
[0.606045, 0.850733, 0.236712],
[0.616293, 0.852709, 0.230052],
[0.626579, 0.854645, 0.223353],
[0.636902, 0.856542, 0.216620],
[0.647257, 0.858400, 0.209861],
[0.657642, 0.860219, 0.203082],
[0.668054, 0.861999, 0.196293],
[0.678489, 0.863742, 0.189503],
[0.688944, 0.865448, 0.182725],
[0.699415, 0.867117, 0.175971],
[0.709898, 0.868751, 0.169257],
[0.720391, 0.870350, 0.162603],
[0.730889, 0.871916, 0.156029],
[0.741388, 0.873449, 0.149561],
[0.751884, 0.874951, 0.143228],
[0.762373, 0.876424, 0.137064],
[0.772852, 0.877868, 0.131109],
[0.783315, 0.879285, 0.125405],
[0.793760, 0.880678, 0.120005],
[0.804182, 0.882046, 0.114965],
[0.814576, 0.883393, 0.110347],
[0.824940, 0.884720, 0.106217],
[0.835270, 0.886029, 0.102646],
[0.845561, 0.887322, 0.099702],
[0.855810, 0.888601, 0.097452],
[0.866013, 0.889868, 0.095953],
[0.876168, 0.891125, 0.095250],
[0.886271, 0.892374, 0.095374],
[0.896320, 0.893616, 0.096335],
[0.906311, 0.894855, 0.098125],
[0.916242, 0.896091, 0.100717],
[0.926106, 0.897330, 0.104071],
[0.935904, 0.898570, 0.108131],
[0.945636, 0.899815, 0.112838],
[0.955300, 0.901065, 0.118128],
[0.964894, 0.902323, 0.123941],
[0.974417, 0.903590, 0.130215],
[0.983868, 0.904867, 0.136897],
[0.993248, 0.906157, 0.143936]]